On parameterized approximation algorithms for balanced clustering

Balanced clustering is a frequently encountered problem in applications requiring balanced class distributions, which generalizes the standard clustering problem in that the number of clients connected to each facility is constrained by the given lower and upper bounds. It was known that both the pr...

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Veröffentlicht in:Journal of combinatorial optimization Jg. 45; H. 1; S. 49
Hauptverfasser: Kong, Xiangyan, Zhang, Zhen, Feng, Qilong
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York Springer US 01.01.2023
Springer Nature B.V
Schlagworte:
Algorithms
Approximation
Clustering
Combinatorics
Convex and Discrete Geometry
Energy consumption
Euclidean space
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Parameterization
Random sampling
Theory of Computation
Upper bounds
Approximation algorithm
Clustering
Parameterized algorithm
ISSN:1382-6905, 1573-2886
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Zusammenfassung:Balanced clustering is a frequently encountered problem in applications requiring balanced class distributions, which generalizes the standard clustering problem in that the number of clients connected to each facility is constrained by the given lower and upper bounds. It was known that both the problems of balanced k -means and k -median are W[2]-hard if parameterized by k , implying that the existences of FPT( k )-time exact algorithms for these problems are unlikely. In this paper, we give FPT( k )-time ( 9 + ϵ ) -approximation and ( 3 + ϵ ) -approximation algorithms for balanced k -means and k -median respectively, improving upon the previous best approximation ratios of 86.9 + ϵ and 7.2 + ϵ obtained in the same time. Our main technical contribution and the crucial step in getting the improved ratios is a different random sampling method for selecting opened facilities.
Bibliographie:ObjectType-Article-1
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ISSN:1382-6905
1573-2886
DOI:10.1007/s10878-022-00980-w